It swings ... Elliott Gould in The Long Goodbye. Photo: Sportsphoto Ltd/Allstar

Every now and then, every national or local film theatre reckons it's time for another season of "Jazz and the Movies". So all the over-cooked chestnuts come out of the fire again: we'll have Clint Eastwood's Bird; Nat King Cole playing WC Handy in St Louis Blues; Sinatra as Frankie Machine in The Man With the Golden Arm; Jazz On a Summer's Day, with Anita O'Day in that hat; Jackie McLean soloing on Shirley Clarke's film of The Connection; Diana Ross as Billie Holiday in Lady Sings the Blues. Are you struggling yet?

It's not that I'd want to exclude all of those films. I know Eastwood has an honourable history with jazz as listener, friend and occasional sketch artist at the piano. But Clint's piano is a lot less interesting than that from the Jeff Bridges character (it's Dave Grusin playing) in The Fabulous Baker Boys (a film that explains why a hip pianist might play garbage for a living instead of risking jazz). I am prepared to say here and now that the immaculate self-promoter and calculating machine in the very white Clint Eastwood is a long way from the experience, character or music of the chaotic but inspired Charlie Parker - too far to make Bird a good film, let alone a decent history of jazz.

All too often, "jazz" at the movies is shorthand for a sordid, sensational and self-destructive lifestyle. Now, the collective history of jazz musicians does support such a view. But sometimes, as you come out of The Man With the Golden Arm, say, vibrating with that insistent score by Elmer Bernstein that is jazz-like without ever catching the air of jazz, you wish that the film's scrappy hero, Frankie Machine, was not a would-be jazz drummer, but a guy longing to be second oboe with the Chicago Symphony.

What I'm trying to suggest is that there may be a deeper, rhythmic bond between film and jazz that surpasses the silly screenwriters' notion that jazz is "hot" or "cool" or ripe for melodrama. I'm thinking about a season that digs into that deeper resemblance, and the wandering soul of improvisation.

This is an area where it's easier to explain the theory with examples, so item one in my season is Elliott Gould in The Long Goodbye, by Robert Altman. No, Gould does not play a jazz musician, and the music on the soundtrack is not exactly jazz, even if the many variations on the John Williams/Johnny Mercer title song are jazzy, in that they have a wit and an experimental ranging that bespeak the inquiring jazz mind when faced with a tune. That's not why I'm including The Long Goodbye - nor do I nominate it because of the directorial presence of Altman, who was from Kansas City, a true centre of jazz. (He actually shot a whole jam session for his movie Kansas City.)

I'm picking Gould because of the loose, liberated, comic spontaneity of his movements, his muttering and his being. Think of that opening scene where he wakes in the middle of the night and faces his cat in a duel over the right cat food. He talks to the cat, he talks to himself, he hums, he groans, he flexes and plays off the frosty alienness of his pet. It's not that he's "cool", or "hip", or a "stoner", though those ideas can be picked up. It's as if this Marlowe - so far from Chandler's very sharp-minded narrator - is a mellow opacity through whom the film is projected. He is like Lester Young, in his room, alone, warming up. He is like Dexter Gordon in Round Midnight. It is one of the great rehearsals in American film, and it swings.

That brings us to an impenetrable wall, described by Duke Ellington: "It don't mean a thing if it ain't got that swing." In other words, if you can watch The Long Goodbye and not get or feel what I'm saying about Gould then, in my estimate, jazz is not for you. Alas and all that, but really the world is full of other things, and jazz is not to be taken lightly. But if you're swinging with Elliott then a feast is in view.

I'd go next to Louis Malle's Lift to the Scaffold. This is the one where Jeanne Moreau and Maurice Ronet are lovers and she expects to meet him at night on the streets of Paris. But he's stuck in the lift! So Malle asks Moreau to stroll and look pensive in Henri Decaë's Tri-X black-and-white photography.

Now, Moreau at this moment was very beautiful. Paris is Paris and Tri-X with urban lighting is one of our more beguiling dreams. Add Miles Davis. The story is that Malle projected the footage of Moreau walking and asked Miles to improvise. The result is riveting, yet it could have worked the other way round - the marriage of the finished film feels just as much as if Jeanne is walking while listening to the Davis music.

One way of describing the result is to say it's "the blues" - a long, linear reverie in which someone faces their own sadness, doubt or anxiety. And here's the real point at which the blues is a mode in art that overlaps with a great deal of poetry, the inwardness of the modern novel, the mutual absorption that can come with some paintings. In other words, the condition On Being Blue (to quote the title of William Gass's great meditation) is something that may be based in music but which applies to a vast array of art. And jazz blues - Kind of Blue or Blues in the Night - is thus one of the essential manifestations of modern experience. It is the solitude that longs for company: it is there in "To be or not to be" as much as in the abandoned desert-like colour mesas by Mark Rothko (which don't have to be blue!).

It may seem that I am making drastic proposals: even that a film about Robin Hood, say, might have a sequence of Robin deep in Sherwood wondering how to get with Marian set against Ben Webster doing Chelsea Bridge. Is that weird, or is the anachronism no more than exists already on The Adventures of Robin Hood (with Errol Flynn), in which the Sherwood days were played against a 1938 studio recording of music by Erich Wolfgang Korngold? The fact that there is often music in the air at the movies only reminds us that the movies are lifelike, but not life.

If you are following this line of thought, then an immense amount of movies are opened up to a jazz interpretation - more or less anything that has a character alone with the camera for a prolonged period guides us into the extended depiction of thought process which is "making it up as you go along", a term that applies equally well to being alive or jazz improvisation.

Consider the extended passage in Otto Preminger's Laura, where the detective (Dana Andrews) spends time alone in Laura's room, mulling over her possessions, sitting beneath the lush portrait of her and slipping into love with her. The music in this scene is not jazz - it's David Raksin's famous tune Laura, given a full-bodied orchestration. But the scene sinks in like sleep. And that's when you begin to realise how far film incorporates a unique soliloquy for the emotional atmosphere of music. A private scene such as this - or like Travis Bickle alone in his room, practising with his guns, talking to the mirror in Taxi Driver - is like a staccato solo by Parker.

Let me add something I associate with Parker. In the late 1950s, on long-playing records, all the takes (some just a few seconds, some the entire number) of his Verve titles were collected. This provided a rare jazz education: the chance to hear a player who believes in variation tackling the same tune or theme over and over again. Without doubt, a real Bird, or a true bop film, would be composed to match the multiple tracks of the Parker classics. If that sounds crazy, look at the work of Jean-Luc Godard in the early 60s, where variation was a vital building block of what are still among the most radical, liberating and musical films ever made.

What I have suggested so far is a new way of seeing jazz on screen and feeling it in life. But there are films, or occasions, where jazz composers have done exceptional work in pictures. The Duke Ellington score for Anatomy of a Murder is the grace notes of a wise man who has understood a very tricky film - just look and listen to the sliding sax section when Lee Remick first appears.

One last thing, the least but the merriest of my points. In the late 1940s, the Canadian animator, Norman McLaren, made a short film, Begone Dull Care, a series of abstracts in which the form and colour of the shapes was driven by the music of Oscar Peterson. No season of jazz and the movies should be without this three and a half minute gem, or without its essential encouragement to us to move. Jazz me, movie.